Conductors and Electric Fields in Static Equilibrium

An electric field due to a positively charged spherical conductor is shown above. Where will the electric field be weakest?

1. Point A
2. Point B
3. Point C
4. Same at all points

(c)

The electric field created by two parallel metal plates is shown above. Where will the electric field be strongest?

1. Point A
2. Point B
3. Point C
4. Same at all points

Suppose that the electric field experienced due to a positively charged small spherical conductor at a certain distance is E. What will be the percentage change in electric field experienced at thrice the distance if the charge on the conductor is doubled?

decrease by 77.78%.

The classic Millikan oil drop experiment setup is shown above. In this experiment oil drops are suspended in a vertical electric field against the gravitational force to measure their charge. If the mass of a negatively charged drop suspended in an electric field of 1.18×10⁻⁴ N/C strength is 3.85×10⁻²¹ g, find the number of excess electrons in the drop.

Is the object in fs-id1586840 a conductor or an insulator? Justify your answer.

If the electric field lines in the figure above were perpendicular to the object, would it necessarily be a conductor? Explain.

The discussion of the electric field between two parallel conducting plates, in this module states that edge effects are less important if the plates are close together. What does close mean? That is, is the actual plate separation crucial, or is the ratio of plate separation to plate area crucial?

Would the self-created electric field at the end of a pointed conductor, such as a lightning rod, remove positive or negative charge from the conductor? Would the same sign charge be removed from a neutral pointed conductor by the application of a similar externally created electric field? (The answers to both questions have implications for charge transfer utilizing points.)

Why is a golfer with a metal club over her shoulder vulnerable to lightning in an open fairway? Would she be any safer under a tree?

Can the belt of a Van de Graaff accelerator be a conductor? Explain.

Are you relatively safe from lightning inside an automobile? Give two reasons.

Discuss pros and cons of a lightning rod being grounded versus simply being attached to a building.

Using the symmetry of the arrangement, show that the net Coulomb force on the charge $q$ at the center of the square below (import-auto-id3009601) is zero if the charges on the four corners are exactly equal.

(a) Using the symmetry of the arrangement, show that the electric field at the center of the square in import-auto-id3009601 is zero if the charges on the four corners are exactly equal. (b) Show that this is also true for any combination of charges in which $q_a=q_d$ and $q_b=q_c$

(a) What is the direction of the total Coulomb force on $q$ in import-auto-id3009601 if $q$ is negative, $q_a=q_c$ and both are negative, and $q_b=q_d$ and both are positive? (b) What is the direction of the electric field at the center of the square in this situation?

Considering import-auto-id3009601, suppose that $q_a=q_d$ and $q_b=q_c$. First show that $q$ is in static equilibrium. (You may neglect the gravitational force.) Then discuss whether the equilibrium is stable or unstable, noting that this may depend on the signs of the charges and the direction of displacement of $q$ from the center of the square.

If $q_a=0$ in import-auto-id3009601, under what conditions will there be no net Coulomb force on $q$?

In regions of low humidity, one develops a special “grip” when opening car doors, or touching metal door knobs. This involves placing as much of the hand on the device as possible, not just the ends of one’s fingers. Discuss the induced charge and explain why this is done.

Tollbooth stations on roadways and bridges usually have a piece of wire stuck in the pavement before them that will touch a car as it approaches. Why is this done?

Suppose a person carries an excess charge. To maintain their charged status can they be standing on ground wearing just any pair of shoes? How would you discharge them? What are the consequences if they simply walk away?

Sketch the electric field lines in the vicinity of the conductor in fs-id2000560 given the field was originally uniform and parallel to the object’s long axis. Is the resulting field small near the long side of the object?

Sketch the electric field lines in the vicinity of the conductor in fs-id2000561 given the field was originally uniform and parallel to the object’s long axis. Is the resulting field small near the long side of the object?

Sketch the electric field between the two conducting plates shown in fs-id765824, given the top plate is positive and an equal amount of negative charge is on the bottom plate. Be certain to indicate the distribution of charge on the plates.

Sketch the electric field lines in the vicinity of the charged insulator in import-auto-id1409558 noting its nonuniform charge distribution.

What is the force on the charge located at $x=\mathrm{8.00\; cm}$ in fs-id1996672(a) given that $q=1\text{.}\text{00}\text{μC}$?

(a) Find the total electric field at $x=\mathrm{1.00\; cm}$ in fs-id1996672(b) given that $q=\mathrm{5.00\; nC}$. (b)Find the total electric field at $x=\mathrm{11.00\; cm}$ in fs-id1996672(b) given that $q=\mathrm{5.00\; nC}$. (c) If the charges are allowed to move and eventually be brought to rest by friction, what will the final charge configuration be? (That is, will there be a single charge, double charge, etc., and what will its value(s) be?)

(a) $2\text{.}\text{12}\times {\text{10}}^5\text{N/C}$

(b) one charge of $+q$

(a) Find the electric field at $x=\mathrm{5.00\; cm}$ in fs-id1996672(a), given that $q=1.00\text{μC}$. (b) At what position between 3.00 and 8.00 cm is the total electric field the same as that for $\mathrm{–2}q$ alone? (c) Can the electric field be zero anywhere between 0.00 and 8.00 cm? (d) At very large positive or negative values of x, the electric field approaches zero in both (a) and (b). In which does it most rapidly approach zero and why? (e) At what position to the right of 11.0 cm is the total electric field zero, other than at infinity? (Hint: A graphing calculator can yield considerable insight in this problem.)

(a) Find the total Coulomb force on a charge of 2.00 nC located at $x=\mathrm{4.00\; cm}$ in fs-id1996672 (b), given that $q=1.00\text{μC}$. (b) Find the x-position at which the electric field is zero in fs-id1996672 (b).

(a) 0.252 N to the left

(b) $x=\mathrm{6.07\; cm}$

Using the symmetry of the arrangement, determine the direction of the force on $q$ in the figure below, given that $q_a=q_b\text{=+}7\text{.}\text{50}\text{μC}$ and $q_c=q_d=-7\text{.}\text{50}\text{μC}$. (b) Calculate the magnitude of the force on the charge $q$, given that the square is 10.0 cm on a side and $q=2\text{.}\text{00}\text{μC}$.

(a) Using the symmetry of the arrangement, determine the direction of the electric field at the center of the square in import-auto-id2617305, given that $q_a=q_b=-1\text{.}\text{00}\text{μC}$ and $q_c=q_d\text{=+}1\text{.}\text{00}\text{μC}$. (b) Calculate the magnitude of the electric field at the location of $q$, given that the square is 5.00 cm on a side.

(a)The electric field at the center of the square will be straight up, since $q_a$ and $q_b$ are positive and $q_c$ and $q_d$ are negative and all have the same magnitude.

(b) $2\text{.}\text{04}\times {\text{10}}^7\text{N/C}\left(\text{upward}\right)$

Find the electric field at the location of $q_a$ in import-auto-id2617305 given that $q_b=q_c=q_d\text{=+}2\text{.}\text{00}\text{nC}$, $q=-1\text{.}\text{00}\text{nC}$, and the square is 20.0 cm on a side.

Find the total Coulomb force on the charge $q$ in import-auto-id2617305, given that $q=1\text{.}\text{00}\text{μC}$, $q_a=2\text{.}\text{00}\text{μC}$, $q_b=-3\text{.}\text{00}\text{μC}$, $q_c=-4\text{.}\text{00}\text{μC}$, and $q_d\text{=+}1\text{.}\text{00}\text{μC}$. The square is 50.0 cm on a side.

$0\text{.}\text{102}\text{N},$ in the $-y$$$$$$$ direction

(a) Find the electric field at the location of $q_a$ in import-auto-id1427585, given that $q_{\text{b}}=\mathrm{+10.00}\mu \text{C}$ and $q_{\text{c}}=\mathrm{–5.00}\mu \text{C}$. (b) What is the force on $q_a$, given that $q_{\text{a}}=\mathrm{+1.50}\text{nC}$?

(a) Find the electric field at the center of the triangular configuration of charges in import-auto-id1427585, given that $q_a\text{=+}2\text{.}\text{50}\text{nC}$, $q_b=-8\text{.}\text{00}\text{nC}$, and $q_c\text{=+}1\text{.}\text{50}\text{nC}$. (b) Is there any combination of charges, other than $q_a=q_b=q_c$, that will produce a zero strength electric field at the center of the triangular configuration?

(a) $\overrightarrow{E}=4.36\times {\text{10}}^3\text{N/C},\mathrm{35.0º}$, below the horizontal.

(b) No